Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect
Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect
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DOI：
10.1016/j.cma.2008.04.018
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发表时间：
2008-01-01
影响因子：
7.2
通讯作者：
Quarteroni, Alfio
中科院分区：
文献类型：
--
作者：
Badia, Santiago;Quaini, Annalisa;Quarteroni, Alfio
本文主要研究具有大附加质量效应的流固耦合问题的数值模拟。我们分析了不同的预条件后得到的耦合系统矩阵的FSI问题的时空离散化和线性化。经典的Dirichlet-Neumann预条件子具有“模块化”的优点，因为它允许以最小的努力（简单的接口通信）重用现有的流体和结构代码。不幸的是，在大的附加质量效应的情况下，它的性能非常差。或者，我们考虑两个非模块化的方法。第一种方法是用适当的对角缩放结合LUT预处理器对耦合系统进行预处理。然后用Krylov方法求解该系统。这个过程的缺点是，流体和结构代码的组合来解决耦合系统是不简单的。我们考虑的第二种非模块化方法是基于线性FSI系统的不精确块LU分解的分裂技术。由此产生的算法计算流体速度分别从耦合的压力-结构系统在每次迭代，降低了计算成本。独立于预处理器，半隐式算法的效率（即，那些以显式方式处理几何和流体非线性的算法）被突出显示，并且将它们的性能与隐式算法之一进行比较。所有的方法都在三维血管系统上进行了测试。结合非模块化ILUT预条件和Krylov方法的算法被证明是最快的。(c)2008 Elsevier B. V.保留所有权利。
In this article we address the numerical simulation of fluid-structure interaction (FSI) problems featuring large added-mass effect. We analyze different preconditioners for the coupled system matrix obtained after space-time discretization and linearization of the FSI problem. The classical Dirichlet-Neumann preconditioner has the advantage of "modularity" because it allows to reuse existing fluid and structure codes with minimum effort (simple interface communication). Unfortunately, its performance is very poor in case of large added-mass effects. Alternatively, we consider two non-modular approaches. The first one consists in preconditioning the coupled system with a suitable diagonal scaling combined with an [LUT preconditioner. The system is then solved by a Krylov method. The drawback of this procedure is that the combination of fluid and structure codes to solve the coupled system is not straightforward. The second non-modular approach we consider is a splitting technique based on an inexact block-LU factorization of the linear FSI system. The resulting algorithm computes the fluid velocity separately from the coupled pressure-structure system at each iteration, reducing the computational cost. Independently of the preconditioner, the efficiency of semi-implicit algorithms (i.e., those that treat geometric and fluid nonlinearities in an explicit way) is highlighted and their performance compared to the one of implicit algorithms. All the methods are tested on three-dimensional blood-vessel systems. The algorithm combining the non-modular ILUT preconditioner with Krylov methods proved to be the fastest. (c) 2008 Elsevier B.V. All rights reserved.